17th Int. Conference onElectrical Drives

andPower ElectronicsThe High Tatras,

Slovakia28-30 September, 2011

Fault-tolerant Control of a Wind Turbinewith a Squirrel-cage Induction Generator

and Rotor Bar DefectsVinko Lesic1), Mario Vasak1), Nedjeljko Peric1), Thomas M. Wolbank2) and Gojko Joksimovic3)

1)Faculty of Electrical Engineering and Computing, University of Zagreb, Zagreb, Croatia2)Faculty of Electrical Engineering and Information Technology, Vienna University of Technology,

Vienna, Austria3)Faculty of Electrical Engineering, University of Montenegro, Podgorica, Montenegro

vinko.lesic@fer.hr, mario.vasak@fer.hr, nedjeljko.peric@fer.hr, thomas.wolbank@tuwien.ac.at, joxo@ac.me

Abstract—Wind turbines are usually installed on remote lo-cations and in order to increase their economic competencemalfunctions should be reduced and prevented. Faults of windturbine generator electromechanical parts are common and veryexpensive. This paper proposes a fault-tolerant control strategy forvariable-speed variable-pitch wind turbines in case of identifiedand characterized squirrel-cage generator rotor bar defect. Anupgrade of the torque control loop with flux-angle-based torquemodulation is proposed. In order to avoid or to postpone generatorcage defects, usage of pitch controller in the low wind speedregion is introduced. Presented fault-tolerant control strategy isdeveloped taking into account its modular implementation andinstallation in available control systems of existing wind turbinesto extend their life cycle and energy production. Simulation resultsfor the case of a 700 kW wind turbine and the identified rotorbar fault are presented.

Index Terms—Wind Turbine Control, Torque Control,Generator-fault-tolerant control

I. INTRODUCTION

Aspiration for finding adequate substitute for conventionalfossil fuel power systems has a great impact on today politi-cal and economic trends and guidelines. Combining differentbranches of science and engineering, wind energy is recognizedas the fastest-growing renewable energy source with an averagegrowth rate of 27% in last 5 years [1]. It is green, inexhaustible,everywhere available but unreliable with poor power qualityand as a result - expensive. The challenge is to make a controlsystem capable of maximizing the energy production and theproduced energy quality while minimizing costs of installationand maintenance.

Wind turbines are usually installed at low-turbulent-windremote locations and it is important to avoid very costlyunscheduled repairs. In order to improve reliability of windturbines, different fault-tolerant control algorithms have beenintroduced [2], focused mainly on sensor, inverter and actuatorfaults. Focus here is on generator electromechanical faults,which are besides gearbox and power converters faults themost common in wind turbine systems [3]. Many installedwind turbines have squirrel-cage induction generator (SCIG)and about 20% to 30% of machine faults are caused by defectsin rotor cage [4].

Rotor bar defect is caused by thermal fatigue due to cyclicthermal stress on the endring-bar connection which occursbecause of different thermal coefficients of bars and laminationsteel. As presented in [5], a monitoring system that is able todetect a developing bar defect is designed based on currentsignature analysis and offers the possibility to change frompreventive to predictive maintenance and thus to significantlysave costs.

Focus of this paper is to research and develop a fault-tolerantextension of the wind turbine control system that prevents theidentified rotor bar defect from spreading. We introduce a fastcontrol loop for flux-angle-based modulation of the generatortorque, and a slow control loop that ensures the generatorplacement at a point that enables the fast loop to performcorrectly and keeps the electrical energy production optimalunder emergency circumstances.

This paper is organized as follows. The basic control strategyfor a variable-speed variable-pitch wind turbine is presentedin Section II along with normal wind turbine operating maps.In Section III a mathematical model of an SCIG is describedexplaining the theoretical basis used to form a control systemextension. A fault-tolerant approach and control algorithmis proposed and described in Section IV that enables windturbine operation in emergency state. Section V provides MAT-LAB/Simulink simulation results obtained with the proposedfault-tolerant control strategy.

II. WIND TURBINE CONTROL SYSTEM

Variable-speed variable-pitch wind turbine operating area isparted into two regions (see Fig. 1): low wind speed region(region I), where all the available wind power is fully capturedand high wind speed region (region II) where the power outputis maintained constant while reducing the aerodynamic torqueand keeping generator speed at the rated value.

The ability of a wind turbine to capture wind energy isexpressed through a power coefficient CP which is defined asthe ratio of extracted power Pt to wind power PV :

CP =PtPV

. (1)

The maximum value of CP , known as Betz limit, is CPmax =1627 = 0.593. It defines the maximum theoretical capability

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364

Vm i n Vm axVN

V (m / s)

Pow

erPN

I I I

PNB

VBmaxVNB

Fig. 1. Ideal power curve with maximum PN and power curve due todeveloped fault with maximum PNB .

of wind power capture. The real power coefficient of moderncommercial wind turbines reaches values of about 0.48 [6].Power coefficient data is usually given as a function of the tip-speed-ratio λ and pitch angle β (Fig. 2). Turbine power andtorque are given by [7]:

Pt = CP (λ, β)PV =1

2ρR2πCP (λ, β)V 3, (2)

Tt =Ptω

=1

2ρR3πCQ(λ, β)V 2, (3)

where CQ = CP /λ, ρ, R, V and ω are torque coefficient,air density, radius of the aerodynamic disk of a wind turbine,wind speed and the angular speed of blades, respectively, andλ = ωR

V .Since the goal is to maximize the output power in low wind

speed region, wind turbine must operate in the area where thepower coefficient CP is at its maximum value (or near it). Thisis achieved by maintaining λ and β on the values that ensureCP = CPmax [6]-[10], see Fig. 2. Therefore the generatortorque and consequently the aerodynamic torque is determinedby:

Tgref =1

2λ3optn3s

ρπR5CPmaxω2g = Kλω

2g , (4)

where ns is the gearbox ratio. This way the wind turbineoperating points in low wind speed region are located atthe maximum output power curve, called CPmax locus. ThisTgref = Kλω

2g torque controller (Fig. 3) can be easily realized

using a simple look-up table.Above designated rated wind speed, the task of the control

system is to maintain the output power of the wind tur-bine constant. It can be done by reducing the aerodynamictorque and angular speed of blades by rotating them alongtheir longitudinal axis (pitching). Consequently, the wind tur-bine power coefficient is reduced. A proportional-integral (PI)or proportional-integral-derivative (PID) controller with gain-

CPmax

30

150

0.5

β λ

0

0

a)

30

15

0

0.08

0

0β λ

b)Fig. 2. Power a) and torque b) coefficients for an exemplary 700 kW variable-pitch turbine.

ωref+-

ω

ω

βref β

Tgref Tg

PITCH servo& controller

SPEEDcontroller

TORQUEcontroller

GENERATOR & INVERTER

WINDWIND

TURBINEω

Fig. 3. Control system of a variable-speed variable-pitch wind turbine.

scheduling technique is often satisfactory for pitch control (Fig.3).

III. MATHEMATICAL MODEL OF AN AC MACHINE

Mathematical model of an AC squirrel-cage induction ma-chine can be represented in a two-phase (d, q) rotating coordi-nate system with following equations [11], [12]:

us = Rsis +dψsdt

+ jωeψs, (5)

0 = Rr ir +dψrdt

+ j(ωe − ωr)ψr. (6)

where bar notation represents a complex (d, q) vector, subscripts stator variables, subscript r rotor variables, i currents andR resistances. In a common rotating coordinate system statorvariables are rotating with speed ωe = 2πf and rotor variableswith speed ωe−ωr, where f is the frequency of the AC voltagesupplied to the stator, ωg is the speed of rotor, ωr = pωg , andp is the number of machine pole pairs. Flux linkages ψs andψr are given by:

ψs = Lsis + Lmir, (7)ψr = Lmis + Lr ir. (8)

where Ls = Lsσ + Lm is stator inductance, Lr = Lrσ + Lmis rotor inductance, and Lm is mutual inductance. ParametersLsσ and Lrσ are stator and rotor flux leakage inductances,respectively. Electromagnetic torque Tg is given by:

Tg = −3

2pLmis × ir. (9)

By introducing a rotor field-oriented control (FOC), rotorflux linkage is in the rotating (d, q) frame fixed as

ψr = ψrd + j0. (10)

Magnetizing current that creates the rotor flux is then definedwith

imr =ψrLm

=ψrdLm

. (11)

By combining (6), (7), (8), (11) and by introducing rotortime constant parameter Tr = Lr

Rr, the following is derived:

isd = imr + Trdimrdt

, (12)

ωsl = ωe − ωr. (13)

where difference between the electrical and mechanical speedis a slip speed defined with ωsl =

isqTrimr

.

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Finally, by combining (7), (8), (9) and (11) electromagnetictorque relation takes the form:

Tg =3

2pL2m

Lrimrisq = kmimrisq. (14)

Relation (14) is the key equation for FOC of an inductionmachine and using rotor FOC isd and isq are fully decoupled.Magnetizing current vector imr is not suitable for fast controlaction influencing torque because of the time lag Tr and istherefore kept constant in the sub-nominal speed operatingregion. Torque is controlled only by q stator current component- isq .

Voltage-controlled machine (Fig. 4) is usually more suitablethan the current-controlled so by substituting (7), (8), (11),(12) into (5) stator voltage vector components usd and usq areobtained:

usd = kaisd + σLsdisddt

− 1

Tr

L2m

Lrimr − ωeσLsisq,(15)

usq = Rsisq + σLsdisqdt

+ ωeL2m

Lrimr + ωeσLsisd.(16)

where ka = (Rs+L2m

L2rRr) and σ = (1− L2

m

LsLr). Relations (15)

and (16) show that d and q coordinates are not fully decoupledand changing the voltage value in one axis, affects also theother. Elements with ωe represent machine back-electromotiveforce (EMF). Since it would be very complicated to controlthese coupled voltages, a decoupling method is applied (see[12]). By introducing correction voltages ∆usd and ∆usq , fullydecoupled relations are derived:

usd + ∆usd = kaisd + σLsdisddt

, (17)

usq + ∆usq = Rsisq + σLsdisqdt

. (18)

These equations are now suitable for further design of thecontrol loop and PI controllers are chosen with integral timeconstants TId = σLs/ka for d-current, TIq = σLs/Rs for q-current and gain Kr. As previously mentioned, in the normalmachine operating region isd is kept constant and imr = isd isimplied. Finally, closed loop dynamics can now be representedas first-order lag system with transfer function:

Tg(s)

Tg REF (s)=

isq(s)

isq REF (s)=

1

1 + τs, (19)

where τ is a time constant defined with τ = σLsKr

.Minimum and maximum torque references that can be ap-

plied to closed loop system, implied by the back EMF andmaximum inverter voltage Umax, are defined respectively with:

T1 =1

Krkg(−Umax − keωe) − T0, (20)

T2 =1

Krkg(Umax − keωe) + T0, (21)

where kg = kmisd, ke = Lsisd and T0 is the torque startingpoint for the transient. Notice that back EMF supports torquereduction and aggravates torque restoration. Because of imr =isd the slip speed is proportional to the torque (or isq current):

ωsl =isq

Trimr=

1

Trkmi2mrTg = kTg. (22)

Tg_REF

isd,isq

ic

ib

ia

SCIG variable +

-

estimation Kr

1+TI sTI s

PI

ωg

(d,q)

(a,b,c)

isd_REF

isq_REF

Umax

+-

Δusd,Δusq

angle

iabc

usd

usq

Fig. 4. Field-oriented control loop.

IV. FAULT-TOLERANT CONTROL

Previous sections have described most widely adopted windturbine control strategies, as well as mathematical model of thegenerator. This section is dedicated for further improvement ofcontrol strategies in order to disable or to postpone generatorfault development and to achieve maximum energy productionunder emergency conditions at the same time. A work thatis focused on stator winding inter-turn short circuit faults forsynchronous machines also appeared recently [13]. For now,detected generator fault triggers a turbine safety device andleads to a system shut-down. Whole unscheduled repair processrequires significant amounts of money and the situation is evenworse for off-shore wind turbines. Not to mention opportunitycosts of turned-off wind turbine.

To avoid thermal stress of the defected rotor bar, currentsflowing through it should be less than currents flowing throughthe healthy ones. The magnitude of currents in rotor bar issinusoidal and it is determined by the machine magnetic flux.Speed at which the flux rotates along the rotor circumferenceis the generator slip speed defined with (13). Flux affects thedamaged rotor bar only on a small part of its path as it movesalong the circumference and is denoted with ∆θ = θ2 − θ1,which corresponds to the angular width of the damaged bar, seeFig. 5. Our primary goal is to reduce the electrical and thermalstress reflected through currents and corresponding generatortorque in that angle span to the maximum allowed safety valueTgf . The value Tgf is determined based on fault identificationthrough machine fault monitoring and characterization tech-niques, together with flux angles θ1 and θ2 [5].

Torque is therefore modulated based on the machine fluxangular position with respect to the damaged part as shown inFig. 5. When the flux in angle θ approaches the angle span∆θ, the torque is reduced to the maximum allowed value Tgfdefined with a fault condition. After the flux passes it, thetorque is restored to the right selected value Tg nonf . The valueTg nonf is determined such that the average machine torque

Rotor flux linkage angle (rad)

Gen

erat

or to

rque

(N

m)

Δθ

Tg_nonf

Tgf

toff t1 t2 ton τπ

(π)(θoff) (θ1) (θ2) (θon)

Tg1(t) Tg2(t)

Fig. 5. Torque modulation due to a fault condition. In brackets are anglesattained at denoted time instant.

EDPE 2011, Stará Lesná, The High Tatras, Slovakia, 28-30 September 2011

366

is maintained on the optimum level, taking into account themachine constraints. Procedure is then periodically executed,with period equal π (or τπ in time domain), since the fluxinfluences the faulty part with its north and south pole in eachturn.

Using the described FOC algorithm with decoupling pro-cedure the generator is modelled as first-order lag system asmentioned in the previous section. Torque transients from Fig.5 are therefore defined as exponential functions, decrease andincrease respectively:

Tg1(t) = e−tτ (Tg nonf − T1) + T1 (23)

Tg2(t) = T2 − e−tτ (T2 − Tgf ) (24)

Slip speed of the generator is defined as

ωsl (Tg (t)) =dθ

dt, (25)

from which the angle is obtained:

θ(t) − θ(0) =

t∫0

ωsl (Tg (t)) dt =

t∫0

kTg (t) dt. (26)

Desired Tgf is reached with transient (23) at certain time t1and desired Tg nonf is reached with transient (24) at certaintime ton:

Tgf = e−t1τ (Tg nonf − T1) + T1, (27)

Tg nonf = T2 − e−tonτ (T2 − Tgf ) + T2. (28)

The angle span which has passed during the torque reductiondetermines the angle θoff at which the transition has to startin order to reach the torque Tgf at angle θ1 due to the finitebandwidth of the torque control loop. In the same way torquerestoration transient determines the angle θon at which thetorque Tg nonf is fully restored. Finally, θoff is derived from(20), (26) and (27):

θoff = θ1 − kτ (Tg nonf − Tgf − T1ln a) , (29)

where ln a = lnTgf−T1

Tg nonf−T1. In the same way, θon is obtained

as:θon = θ2 + kτ (Tgf − Tg nonf − T2ln b) , (30)

where ln b = lnT2−Tg nonfT2−Tgf .

If the torque value Tg nonf can be restored at some anglethen the following relation holds:

θon − θoff 6 π. (31)

Putting (29) and (30) into (31), the following is obtained forcondition (31):

−kτ (T1 ln a+ T2 ln b) 6 π − ∆θ. (32)

Because of large inertia of the whole drivetrain, generatorand blade system, described torque oscillations (reduction andrestoration) are barely noticeable on the speed transient, suchthat the wind turbine shaft perceives the mean torque value:

Tav =1

τπ

τπ∫0

Tgdt. (33)

Mean value of the generator torque from Fig. 5 is then givenby:

Tav =π − 2kτ (T1 ln a+ T2 ln b)

kτπ, (34)

with

τπ =π − ∆θ + kτ (T1 ln a+ T2 ln b)

kTg nonf−

−τ (ln a+ ln b) +∆θ

kTgf. (35)

Equation (31) (or (32)) is not satisfied if the speed ωg is largeenough (or if there is a large rotor path under fault influence).In that case the torque modulation is given with Fig. 6 andpeak torque T ∗

g is attained at angle θ∗:

θ2 − π + kτ(Tgf − T ∗

g − T2 ln b∗)

=

= θ1 − kτ(T ∗g − Tgf − T1 ln a∗

)(36)

where ln a∗ = lnTgf−T1

T∗g−T1and ln b∗ = ln

T2−T∗gT2−Tgf . Values T ∗

g

and θ∗ can be obtained from:

kτ (T1 ln a∗ + T2 ln b∗) = ∆θ − π (37)

θ∗ = θ1 − kτ(T ∗g − Tgf − T1ln a∗

). (38)

Mean value of the generator torque from Fig. 6 (i.e. in casewhen (31) is not satisfied) is now given by

Tav =π − kτ (T1 ln a∗ + T2 ln b∗)

kτ∗π, (39)

withτ∗π = −τ (ln a∗ + ln b∗) +

∆θ

kTgf. (40)

Concludingly, if (32) is fulfilled, the resulting average torqueis given with (34); if not, then the resulting average torque isgiven with (39). On the boundary, i.e. for equality in (31) or(32), both (34) and (39) give the same torque Tav , such thatTav(ωg) is continuous. The maximum available torque Tg nonfis the nominal generator torque Tgn. Replacing Tg nonf in (34)with the nominal generator torque Tgn gives the maximumavailable average torque under fault characterized with ∆θ andTgf . Fig. 7 shows an exemplary graph of available speed-torquepoints under machine fault, where the upper limit is based onrelations (32), (34) and (39) with Tg nonf = Tgn. Dashed areadenotes all available average generator torque values that canbe achieved for certain generator speed.

Gen

erat

or to

rque

(N

m)

Δθ

Rotor flux linkage angle (rad)

Tg*

Tgf

t* t1 t2 τπ

(π)(θ*) (θ1 ) (θ2 )*

Tg1(t)Tg2(t)

Fig. 6. Torque modulation due to a fault condition when Tg nonf cannot berestored.

EDPE 2011, Stará Lesná, The High Tatras, Slovakia, 28-30 September 2011

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From Fig. 7 it follows that up to the speed ωg1 it is possibleto control the wind turbine in the faulty case without sacrificingpower production. However, from that speed onwards it is nec-essary to use blades pitching in order to limit the aerodynamictorque and to keep the power production below optimal in orderto suppress the fault from spreading. The speed control loop ismodified such that instead of reference ωn the reference ω1 (incase of gearbox, ω1 = ωg1/ns) is selected. This activates pitchcontrol once the right edge of the feasible-under-fault optimaltorque characteristics is reached. The optimal power point onTav(ωg), which is always on the upper edge of the dashed area,may deviate from this point and thus further improvementsin power production outside the point (ωg1, Tav (ωg1)) maybe obtained by using maximum power tracking control alongthe curve of maximum Tav in the speed span [ωg1, ωgn]. Theinterventions in classical wind turbine control that ensure fault-tolerant control are given in Fig. 8. Algorithms of the slow andthe fast fault-tolerant control loop are given in the sequel.

1) Fault-tolerant control algorithm, slow loop:I. If T

′

gref ≤ Tgf , disable the fast loop and pass T′

gref tothe torque controller;

II. Compute Tg nonf from (20), (21), (34) and (35) such thatTav(ωg) = T

′

gref ; if Tg nonf > Tgn, set Tg nonf = Tgn;III. If (32) is fulfilled set θstart = θoff modπ and θend = θon

else compute θ∗ from (38) and set θstart = θ∗ mod π,θend = θ2 and Tg nonf = T2;

IV. Compute ωg1 as a speed coordinate of the intersectionpoint of Tav(ωg) and of the normal wind turbine torquecontroller characteristics, compute ω1 = ωg1/ns and setωref = ω1.

2) Fault-tolerant control algorithm, fast loop:I. On the positive edge of logical conditions:

• θ > θstart set Tgref = T1,• θ > θ1 set Tgref = Tgf ,• θ > θ2 set Tgref = T2,• θ > θend set Tgref = Tg nonf .

V. SIMULATION RESULTS

This section provides simulation results for a 700 kWMATLAB/Simulink variable-speed variable-pitch wind turbine

0 10 20 300

50

100

150

200

250Tgn

Tgf

Tav

Tgopt

ωg1

Speed (rpm)

Ge

ne

rato

r to

rqu

e (

kNm

) Healthy machine

Faulty machine

ωgn

Fig. 7. Available torque-speed generator operating points under fault condition(shaded area). Full line is the achievable part of the wind turbine torque-speedcurve under faulty condition. Dash-dot line is the healthy machine curve.

TORQUEcontroller

GENERATOR & INVERTER

WIND

FAULT-TOLERANT control

ωref

ω

ω

β

Tg

WINDTURBINE

ω

Tgref'

βref PITCH servo& controller

SPEEDcontroller

ωg

Tgref

θ

+-

FASTloop

SLOWloop

Fault detection and characterization

Tgref'

ωg

Tg_nonfTgref

TgfTgf θ1,θ2

θ

ωref

a)

b)

θstart

θend

T ,1 T2

Fig. 8. a) Control system of wind turbine with fault-tolerant control strategy.b) Enlarged fault-tolerant control block.

model with a two-pole 5.5 kW SCIG scaled to match the torqueof 700 kW machine. Generator parameters are: Ls = Lr =0.112 H, Lm = 0.11 H, Rs = 0.3304 Ω, Rr = 0.2334 Ωand PI controller gain is Kr = 1. Turbine parameters are:CPmax = 0.4745, R = 25 m, λopt = 7.4, ωn = 29rpm, Ttn = 230.5 kNm with gearbox ratio ns = 105.77.Maximum voltage of DC-link is Umax = 214 V. Fault issimulated between flux angles θ1 = π

2 and θ2 = π2 + π

5 , withTgf = 0.5Tgn and presented fault-tolerant control algorithm isapplied. Results in Fig. 9 show how the wind turbine behaves inhealthy and faulty condition for a linear change of wind speedthrough the entire wind turbine operating area.

Fig. 10 shows the fault-tolerant control system reaction tothe fault that is identified at t = 40 s for the case when theaverage generator torque under fault Tav(ωg) can be equal tothe required torque T

′

gref for the incurred speed ωg , i.e. theoptimum speed-torque point is for the occurred fault in thedashed area of Fig. 7, above the line Tg = Tgf .

Fig. 11 shows the fault-tolerant control system reaction tothe fault identified at t = 40 s for the case when the incurredhealthy machine speed-torque operating point falls out of thedashed area of Fig. 7. In this case blade pitching is used in thefaulty condition to bring the speed-torque operating point into(ωg1, Tav(ωg1)).

Fig. 12 shows the influence of fast loop reference switchingon generator currents (and torque). This way the time neededfor torque transients is reduced to minimum possible valuekeeping wind turbine in low-energy production operation aslittle as possible under emergency circumstances.

VI. CONCLUSIONS

This paper introduces a fault-tolerant control scheme forvariable-speed variable-pitch wind turbines with a squirrel-cage generator. We focus on generator rotor bar defect thatcan be characterized at early stage of development. A simpleextension of the conventional control structure is proposed thatprevents the fault propagation while power delivery under fault

EDPE 2011, Stará Lesná, The High Tatras, Slovakia, 28-30 September 2011

368

Fig. 9. Wind turbine power production and pitch angle for healthy and faultyconditions.

Fig. 10. Generator torque modulation and wind turbine speed whenTg nonf < Tgn. Fault occurs at 40 s.

35 40 45 50 55 60100

150

200

250

Time (s)

Generator torque (kNm)

35 36 37 38 39 40 41 42 43 44 45100

150

200

250

35 40 45 50 55 6027

27.5

28

28.5

29

29.5

Fig. 11. Generator torque modulation and wind turbine speed whenTg nonf = Tgn. Fault occurs at 40 s.

40.2 40.25 40.3 40.35 40.4 40.45 40.5 40.555

10

15

20

Fig. 12. Quadrature current component.

is deteriorated as less as possible compared to healthy machineconditions.

ACKNOWLEDGEMENT

This work has been supported by the European Commissionand the Republic of Croatia under grant FP7-SEE-ERA.netPLUS ERA 80/01.

REFERENCES

[1] World Wind Energy Association. (2010). World wind energy installedcapacity [Online]. Available: http://www.wwindea.org

[2] S. Pourmohammad, A. Fekih, ”Fault-Tolerant Control of Wind TurbineSystems - A Review”,Proc. of the 2011. IEEE Green Technologies Con-ference (IEEE-Green), April 2011.

[3] Z. Daneshi-Far, G. A. Capolino, H. Henao, ”Review of Failures andCondition Monitoring in Wind Turbine Generators”, XIX InternationalConference on Electrical Machines - ICEM 2010, September 2010.

[4] A. H. Bonnet and C. Yung, Increased efficiency versus increased reliability,IEEE Industry Applications Magazine, vol.14, no.1, pp.29-36, 2008.

[5] G. Stojicic, P. Nussbaumer, G. Joksimovic, M. Vasak, N. Peric and T. M.Wolbank, ”Precise Separation of Inherent Induction Machine Asymmetriesfrom Rotor Bar Fault Indicator”, 8th IEEE International Symposiumon Diagnostics for Electrical Machines, Power Electronics & Drives,SDEMPED, 2011.

[6] M. Jelavic, N. Peric, I. Petrovic, M. Kajari and S. Car, ”Wind turbine con-trol system”, Proc. of the 7th Symposium on Power System Management,HO CIGRE, November 2006, pp. 196-201.

[7] F. D. Bianchi, H. De Battista and R. J. Mantz, Wind Turbine ControlSystems - Principles, Modelling and Gain Scheduling Design., London,England: Springer, ISBN 1-84628-492-9, 2007.

[8] T. Burton, D. Sharpe, N. Jenkins and E. Bossanyi Wind Energy Handbook,England: John Wiley & Sons, ISBN 0-471-48997-2, 2001.

[9] L. Y. Pao and K. E. Johnson, ”Control of Wind Turbines: Approaches,Challenges, and Recent Developments”, IEEE Control Systems Magazinevol. 31, no. 2, April 2011, pp. 44-62.

[10] F. Blaabjerg, F. Iov, R. Teodorescu and Z. Chen. ”Power Electronicsin Renewable Energy Systems” Proc. of the 12th International PowerElectronics and Motion Control Conf. (EPE-PEMC 2006), 2006.

[11] W. Leonhard, Control of Electrical Drives, Berlin, Germany: SpringerVerlag, ISBN 3-540-41820-2, 2001.

[12] M. P. Kazmierkowski, F. Blaabjerg and R. Krishnan, Control in PowerElectronics - Selected Problems, San Diego, California: Academic Press,An imprint of Elsevier Science, ISBN 0-12-402772-5, 2002.

[13] V. Lesic, M. Vasak, T. M. Wolbank, G. Joksimovic, N. Peric, ”Fault-Tolerant Control of a Blade-pitch Wind Turbine With Inverter-fed Gener-ator”, 20th IEEE International Symposium on Industrial Electronics, ISIE,June 2011, pp. 2097-2102.

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